Question

The difference between two numbers is 48.the ratio of two numbers is 7:3.what are the two numbers?

Answer 1

Let the numbers be a and b
a-b = 48
and, a/b = 7/3
⇒3a = 7b
⇒a = 7b/3

substituting the value,
7b/3 - b = 48
⇒4b/3 = 48
⇒b = 36
so, a = (7×36)/3 = 84

Answer 2

let,
the two numbers = x and y
according to the question,
x - y  = 48..........(1)
ratio of the numbers = 7 : 3
x/y = 7/3
3x = 7y
  x = 7/3 y...........(2)
sub (2) in (1)
we get,
7/3 y - y = 48
(7y-3y) / 3 = 48
4y = 144
y = 36.....(3)
sub (3) in (1)
we get,
x-  36 = 48
x = 48+ 36
x = 84